This invention relates to a continuous process to extract radioactive metal from incinerator ash and other high-residue waste materials using a cocurrent/countercurrent contactor system. The process achieves nearly complete extraction of the metal, water-washing removal of residual nitric acid extractant, and drying of residues in one continuous operation. A cocurrent reactor means is used in order to overcome a swelling or foaming reaction that would severely limit throughput capability of an all-countercurrent system.